This paper surveys the field of asset pricing. The emphasis is on the interplay between theory and empirical work and on the trade-off between risk and return. Modern research seeks to understand the behavior of the stochastic discount factor ~SDF! that prices all assets in the economy. The behavior of the term structure of real interest rates restricts the conditional mean of the SDF, whereas patterns of risk premia restrict its conditional volatility and factor structure. Stylized facts about interest rates, aggregate stock prices, and cross-sectional patterns in stock returns have stimulated new research on optimal portfolio choice, intertemporal equilibrium models, and behavioral finance. This paper surveys the field of asset pricing. The emphasis is on the interplay between theory and empirical work. Theorists develop models with testable predictions; empirical researchers document “puzzles”—stylized facts that fail to fit established theories—and this stimulates the development of new theories. Such a process is part of the normal development of any science. Asset pricing, like the rest of economics, faces the special challenge that data are generated naturally rather than experimentally, and so researchers cannot control the quantity of data or the random shocks that affect the data. A particularly interesting characteristic of the asset pricing field is that these random shocks are also the subject matter of the theory. As Campbell, Lo, and MacKinlay ~1997, Chap. 1, p. 3! put it: What distinguishes financial economics is the central role that uncertainty plays in both financial theory and its empirical implementation. The starting point for every financial model is the uncertainty facing investors, and the substance of every financial model involves the impact of uncertainty on the behavior of investors and, ultimately, on mar-* Department of Economics, Harvard University, Cambridge, Massachusetts

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We present a novel approach to dynamic portfolio selection that is as easy to implement as the static Markowitz paradigm. We expand the set of assets to include mechanically managed portfolios and optimize statically in this extended asset space. We consider “conditional” portfolios, which invest in each asset an amount proportional to conditioning variables, and “timing” portfolios, which invest in each asset for a single period and in the risk-free asset for all other periods. The static choice of these managed portfolios represents a dynamic strategy that closely approximates the optimal dynamic strategy for horizons up to 5 years.

After years of relative neglect in academic circles, portfolio choice problems are again at the forefront of financial research. The economic theory underlying an investor’s optimal

Recent research in empirical finance has documented that expected excess returns on bonds and stocks, real interest rates, and risk shift over time in predictable ways. Furthermore, these shifts tend to persist over long periods of time. This paper has two objectives. First, we propose an empirical model that is able to capture the complex dynamics of expected returns and risk, yet is simple to apply in practice. Second, we explore the implications for asset allocation. Changes in investment opportunities have the important implication that the risk-return tradeoff of bonds, stocks, and cash may be significantly different across investment horizons, thus creating a “term structure of the risk-return tradeoff. ” We show how one can easily extract this term structure using our parsimonious model of return dynamics, and illustrate our approach using data from the U.S. stock and bond markets. We find that asset return predictability has important effects on the variance and correlation structure of returns on stocks, bonds and T-bills across investment horizons. Recent research in empirical finance has documented that expected excess returns on bonds and stocks, real interest rates, and risk shift over time in predictable ways. Furthermore, these shifts tend to persist over long periods of time. Starting at least

We consider the consumption and portfolio choice problem of a long-run investor when the term structure is affine and when the investor has access to nominal bonds and a stock portfolio. In the presence of unhedgeable inflation risk, there exist multiple pricing kernels that produce the same bond prices, but a unique pricing kernel equal to the marginal utility of the investor. We apply our method to a three-factor Gaussian model with a time-varying price of risk that captures the failure of the expectations hypothesis seen in the data. We extend this model to account for time-varying expected inflation, and estimate the model with both inflation and term structure data. The estimates imply that the bond portfolio for the long-run investor looks very different from the portfolio of a mean-variance optimizer. In particular, the desire to hedge changes in term premia generates large hedging demands for long-term bonds. 2 1

This paper studies strategic asset allocation and consumption choice in the presence of regime switching in asset returns. We find evidence that four separate regimes- characterized as crash, slow growth, bull and recovery states- are required to capture the joint distribution of stock and bond returns. Optimal asset allocations vary considerably across these states- both among bonds and stocks and among large and small stocks- and change over time as investors revise their estimates of the underlying state probabilities. In the crash state investors always allocate more of their portfolio to stocks the longer their investment horizon, while the optimal allocation to stocks declines as a function of the investment horizon in bull markets. The joint effects of learning about the underlying state probabilities and predictability of asset returns from the dividend yield give rise to a non-monotonic relationship between the investment horizon and the demand for stocks. Consumption-to-wealth ratios are found to depend on the underlying state and welfare costs from ignoring regime switching are substantial even after accounting for parameter uncertainty. Out-of-sample forecasting experiments confirmtheeconomicimportanceof accounting for the presence of regimes in asset returns. We are grateful to John Campbell for discussion and also thank seminar participants at Caltech, the Innovations in Financial

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The covariance between US Treasury bond returns and stock returns has moved considerably over time. While it was slightly positive on average in the period 1953— 2005, it was particularly high in the early 1980’s and negative in the early 2000’s. This paper specifies and estimates a model in which the nominal term structure of interest ratesisdrivenbyfive state variables: the real interest rate, risk aversion, temporary and permanent components of expected inflation, and the covariance between nominal variables and the real economy. The last of these state variables enables the model to fit the changing covariance of bond and stock returns. Log nominal bond yields and term premia are quadratic in these state variables, with term premia determined mainly by the product of risk aversion and the nominal-real covariance. The concavity of the yield curve–the level of intermediate-term bond yields, relative to the average of short- and long-term bond yields–is a good proxy for the level of term premia. The nominal-real covariance has declined since the early 1980’s, driving down term